Question: Daniel is 32 years younger than Emily. Nine years ago, Emily was 5 times as old as Daniel. How old is Emily now?
Solution: We can use the given information to write down two equations that describe the ages of Emily and Daniel. Let Emily's current age be $e$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $e = d + 32$ Nine years ago, Emily was $e - 9$ years old, and Daniel was $d - 9$ years old. The information in the second sentence can be expressed in the following equation: $e - 9 = 5(d - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$ , we get: $d = e - 32$ . Substituting this into our second equation, we get the equation: $e - 9 = 5($ $(e - 32)$ $ -$ $ 9)$ which combines the information about $e$ from both of our original equations. Simplifying the right side of this equation, we get: $e - 9 = 5e - 205$ Solving for $e$ , we get: $4 e = 196$ $e = 49$.